Synchronization in Relaxation Oscillator Networks with Conduction Delays

2001 ◽  
Vol 13 (5) ◽  
pp. 1003-1021 ◽  
Author(s):  
Jeffrey J. Fox ◽  
Ciriyam Jayaprakash ◽  
DeLiang Wang ◽  
Shannon R. Campbell
Keyword(s):  
Numerical Simulations ◽  
Coupled Oscillators ◽  
Initial Conditions ◽  
Relaxation Oscillator ◽  
Phase Lag ◽  
Relaxation Oscillators ◽  
Oscillator Networks ◽  
Coupled Networks ◽  
Parameter Values ◽  
Zero Phase

We study locally coupled networks of relaxation oscillators with excitatory connections and conduction delays and propose a mechanism for achieving zero phase-lag synchrony. Our mechanism is based on the observation that different rates of motion along different nullclines of the system can lead to synchrony in the presence of conduction delays. We analyze the system of two coupled oscillators and derive phase compression rates. This analysis indicates how to choose nullclines for individual relaxation oscillators in order to induce rapid synchrony. The numerical simulations demonstrate that our analytical results extend to locally coupled networks with conduction delays and that these networks can attain rapid synchrony with appropriately chosen nullclines and initial conditions. The robustness of the proposed mechanism is verified with respect to different nullclines, variations in parameter values, and initial conditions.

Experimental results on synchronization times and stable states in locally coupled light-controlled oscillators

2009 ◽  
Vol 367 (1901) ◽  
pp. 3267-3280 ◽  
Author(s):  
Nicolas Rubido ◽  
Cecilia Cabeza ◽  
Arturo C. Martí ◽  
Gonzalo Marcelo Ramírez Ávila
Keyword(s):  
Numerical Simulations ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Initial Conditions ◽  
Experimental Studies ◽  
Numerical Results ◽  
Experimental Results ◽  
Stable States ◽  
Relaxation Oscillators ◽  
Local Coupling

Recently, a new kind of optically coupled oscillators that behave as relaxation oscillators has been studied experimentally in the case of local coupling. Even though numerical results exist, there are no references about experimental studies concerning the synchronization times with local coupling. In this paper, we study both experimentally and numerically a system of coupled oscillators in different configurations, including local coupling. Synchronization times are quantified as a function of the initial conditions and the coupling strength. For each configuration, the number of stable states is determined varying the different parameters that characterize each oscillator. Experimental results are compared with numerical simulations.

Inviscid quasi-geostrophic flow over topography: testing statistical mechanical theory

1996 ◽  
Vol 309 ◽  
pp. 85-91 ◽  
Author(s):  
William J. Merryfield ◽  
Greg Holloway
Keyword(s):  
Numerical Simulations ◽  
Large Range ◽  
Initial Conditions ◽  
Steady Flows ◽  
Mechanical Theory ◽  
Geostrophic Flow ◽  
Mechanical Description ◽  
Flow Over Topography ◽  
Statistical Mechanical ◽  
Parameter Values

Numerical simulations are employed in a detailed test of the statistical mechanical description of topographic turbulence. Predictions of steady flows correlated with topography are given particular attention. Agreement between numerical and statistical mechanical results is demonstrated for a large range of parameter values, and over an ensemble of random choices of topography and initial conditions.

IMPOSSIBILITY OF ASYMPTOTIC SYNCHRONIZATION FOR PULSE-COUPLED OSCILLATORS WITH DELAYED EXCITATORY COUPLING

2009 ◽  
Vol 19 (06) ◽  
pp. 425-435 ◽  
Author(s):  
WEI WU ◽  
TIANPING CHEN
Keyword(s):  
Coupled Oscillators ◽  
East Asian ◽  
Coupled Oscillator ◽  
Dynamic Behaviors ◽  
Transmission Delays ◽  
Oscillator Networks ◽  
Coupled Networks ◽  
Pulse Coupled Oscillators ◽  
Asymptotic Synchronization ◽  
Coupled Oscillator Model

Fireflies, as one of the most spectacular examples of synchronization in nature, have been investigated widely. In 1990, Mirollo and Strogatz proposed a pulse-coupled oscillator model to explain the synchronization of South East Asian fireflies (Pteroptyx malaccae). However, transmission delays were not considered in their model. In fact, when transmission delays are introduced, the dynamic behaviors of pulse-coupled networks change a lot. In this paper, pulse-coupled oscillator networks with delayed excitatory coupling are studied. A concept of synchronization, named weak asymptotic synchronization, which is weaker than asymptotic synchronization, is proposed. We prove that for pulse-coupled oscillator networks with delayed excitatory coupling, weak asymptotic synchronization cannot occur.

THE DYNAMICS OF TWO PULSE-COUPLED RELAXATION OSCILLATORS

1992 ◽  
Vol 02 (02) ◽  
pp. 341-352 ◽  
Author(s):  
ADAM A. BRAILOVE
Keyword(s):  
Natural Frequencies ◽  
Initial Conditions ◽  
Periodic Trajectory ◽  
Realistic Case ◽  
Relaxation Oscillators ◽  
Integrate And Fire ◽  
Necessary And Sufficient ◽  
Parameter Values

The dynamics of a pair of coupled integrate-and-fire oscillators is studied. Previous work by Mirollo and Strogatz is extended here to include the more realistic case in which the oscillators have different natural frequencies. It is shown that, given sufficient coupling, oscillators with arbitrary natural frequencies can always be made to synchronize. Furthermore, the condition necessary and sufficient for synchronization is determined. It is also shown that for any given set of parameter values there is a single periodic trajectory toward which all initial conditions are attracted: neither chaos nor quasiperiodicity is possible.

scholarly journals The Impact of Initial Conditions in N-Body Simulations of Debris Discs

2015 ◽  
Vol 32 ◽  
Author(s):  
E. Thilliez ◽  
S. T. Maddison
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Parent Body ◽  
Dust Trapping ◽  
Physical Context ◽  
Disc Width ◽  
Wide Range ◽  
Belt Width ◽  
New Generation ◽  
The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

Delay stabilization of periodic orbits in coupled oscillator systems

2010 ◽  
Vol 368 (1911) ◽  
pp. 319-341 ◽  
Author(s):  
B. Fiedler ◽  
V. Flunkert ◽  
P. Hövel ◽  
E. Schöll
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Periodic Orbits ◽  
Coupled Oscillators ◽  
Coupled Oscillator ◽  
Non Invasive ◽  
Coupling Parameters ◽  
Necessary And Sufficient ◽  
Time Delayed Feedback ◽  
Coupled Oscillator Systems

We study diffusively coupled oscillators in Hopf normal form. By introducing a non-invasive delay coupling, we are able to stabilize the inherently unstable anti-phase orbits. For the super- and subcritical cases, we state a condition on the oscillator’s nonlinearity that is necessary and sufficient to find coupling parameters for successful stabilization. We prove these conditions and review previous results on the stabilization of odd-number orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.

scholarly journals Predicting Experimental Sepsis Survival with a Mathematical Model of Acute Inflammation

2021 ◽  
Vol 1 ◽  
Author(s):  
Jared Barber ◽  
Amy Carpenter ◽  
Allison Torsey ◽  
Tyler Borgard ◽  
Rami A. Namas ◽  
...  
Keyword(s):  
Immune Response ◽  
Growth Rate ◽  
Inflammatory Response ◽  
Inflammatory Responses ◽  
Initial Conditions ◽  
Mortality Data ◽  
Experimental Sepsis ◽  
Initial Inoculum ◽  
Molecular Pattern ◽  
Parameter Values

Sepsis is characterized by an overactive, dysregulated inflammatory response that drives organ dysfunction and often results in death. Mathematical modeling has emerged as an essential tool for understanding the underlying complex biological processes. A system of four ordinary differential equations (ODEs) was developed to simulate the dynamics of bacteria, the pro- and anti-inflammatory responses, and tissue damage (whose molecular correlate is damage-associated molecular pattern [DAMP] molecules and which integrates inputs from the other variables, feeds back to drive further inflammation, and serves as a proxy for whole-organism health status). The ODE model was calibrated to experimental data from E. coli infection in genetically identical rats and was validated with mortality data for these animals. The model demonstrated recovery, aseptic death, or septic death outcomes for a simulated infection while varying the initial inoculum, pathogen growth rate, strength of the local immune response, and activation of the pro-inflammatory response in the system. In general, more septic outcomes were encountered when the initial inoculum of bacteria was increased, the pathogen growth rate was increased, or the host immune response was decreased. The model demonstrated that small changes in parameter values, such as those governing the pathogen or the immune response, could explain the experimentally observed variability in mortality rates among septic rats. A local sensitivity analysis was conducted to understand the magnitude of such parameter effects on system dynamics. Despite successful predictions of mortality, simulated trajectories of bacteria, inflammatory responses, and damage were closely clustered during the initial stages of infection, suggesting that uncertainty in initial conditions could lead to difficulty in predicting outcomes of sepsis by using inflammation biomarker levels.

scholarly journals Near-zero phase-lag hyperscanning in a novel wireless EEG system

2021 ◽  
Author(s):  
Chun-Hsiang Chuang ◽  
Shao-Wei Lu ◽  
Yiping Chao ◽  
Po-Hsun Peng ◽  
Hao-Che Hsu ◽  
...  
Keyword(s):  
Phase Lag ◽  
Wireless Eeg ◽  
Zero Phase

Dynamics of Dual-Cell Series Miura-Ori Structures With Different Types of Inter-Cell Connections

2021 ◽  
Author(s):  
Hai Zhou ◽  
Haiping Wu ◽  
Jian Xu ◽  
Hongbin Fang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Theoretical Basis ◽  
Initial Conditions ◽  
Cell Structure ◽  
Dynamic Responses ◽  
Complex Environment ◽  
Current State ◽  
Different Types ◽  
Cell Series

Abstract Origami-inspired structures and materials have shown remarkable properties and performances originating from the intricate geometries of folding. Origami folding could be a dynamic process and origami structures could possess rich dynamic characteristics under external excitations. However, the current state of dynamics of origami has mostly focused on the dynamics of a single cell. This research has performed numerical simulations on multi-stable dual-cell series Miura-Ori structures with different types of inter-cell connections based on a dynamic model that does not neglect in-plane mass. We introduce a concept of equivalent constraint stiffness k* to distinguish different types of inter-cell connections. Results of numerical simulations reveal the multi-stable dual-cell structure will exhibit a variety of complex nonlinear dynamic responses with the increasing of connection stiffness because of the deeper energy well it has. The connection stiffness has a strong effect on the steady-state dynamic responses under different excitation amplitudes and a variety of initial conditions. This effect makes us able to adjust the dynamic behaviors of dual-cell series Miura-Ori structure to our needs in a complex environment. Furthermore, the results of this research could provide us a theoretical basis for the dynamics of origami folding and serve as guidelines for designing dynamic applications of origami metastructures and metamaterials.

Effects of local oscillator frequency on intersegmental coordination in the lamprey locomotor CPG: theory and experiment

1996 ◽  
Vol 76 (6) ◽  
pp. 4094-4103 ◽  
Author(s):  
K. A. Sigvardt ◽  
T. L. Williams
Keyword(s):  
Coupled Oscillators ◽  
Intact Animal ◽  
Local Oscillator ◽  
Ventral Root ◽  
Phase Lag ◽  
Intersegmental Coordination ◽  
Glutamate Concentration ◽  
Phase Lags ◽  
Theory And Experiment

1. Experiments have been performed on in vitro preparations of lamprey spinal cord bathed in D-glutamate, which induces a pattern of activity recorded from ventral roots that is similar to that seen in the intact animal during swimming. The frequency of fictive swimming increases with increasing D-glutamate concentration, but intersegmental phase lag remains unaffected. 2. The effects on intersegmental phase lags of unequal activation of the rostral and caudal halves of a preparation were determined. Unequal activation was produced by placing a diffusion barrier in the middle of the chamber and perfusing the two halves with different concentrations of D-glutamate. 3. Within the rostral compartment, the phase lag increased from control when the rostral D-glutamate concentration was higher than the caudal concentration, and decreased from control when it was lower. By contrast, the phase lags within the caudal compartment did not depend on the ratio of D-glutamate concentration between the two compartments. 4. The frequency of the ventral root activity during differential activation was not significantly different from that of control experiments that had the same concentration as in the rostral compartment. 5. The results are discussed within the context of the mathematical analysis of chains of coupled oscillators by Kopell and Ermentrout and other current theories about the mechanisms of intersegmental coordination in the lamprey.

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